Unformatted text preview: 24. Make a graph where vertices correspond to cities and an edge signifies that the corresponding cities are within 150 km and, therefore, must be assigned different channels. The number of channels required is the chromatic number of the graph which, in this problem, is five, as shown. (Note that the graph contains K 5 ; vertices A, B, D, F and H.) 25. No new channel is required since the chromatic number of the new graph is still five. City J can be assigned the same channel as E and F. 4 F B 1 26. (a) [BB] The dual of the cube is the octahedron whose graph appears in Fig. 13.5. (b) The dual of the dodecahedron is the icosahedron whose graph appears in Fig. 10.19. 27. [BB] Yes, it is. Both the tetrahedron and its dual are K4. Exercises 13.3 1. (a) [BB] 36 nodes, 14 grid segments, 6 nets. (c) [BB]...
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 Summer '10
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 Graph Theory, Polyhedron, vertices, Platonic solid, nd vertex attacks

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